What is the solution for (d^2y)/(dx^2)+2/x (dy)/(dx)=3x+4 ?

The solution for (d^2y)/(dx^2)+2/x (dy)/(dx)=3x+4 is y=c_{1}+(c_{2})/x+(3x^3+8x^2)/(12)

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(d^2y)/(dx^2)+2/x (dy)/(dx)=3x+4

\frac{d ^{2} y}{d x ^{2}} + \frac{2}{x} \frac{d y}{d x} = 3 x + 4

y = c_{1} + \frac{c _{2}}{x} + \frac{3 x ^{3} + 8 x ^{2}}{12}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{2}{x} \frac{d y}{d x} = 3 x + 4

Solve linear ODE:

y = c_{1} + \frac{c _{2}}{x} + \frac{3 x ^{3} + 8 x ^{2}}{12}

y = c_{1} + \frac{c _{2}}{x} + \frac{3 x ^{3} + 8 x ^{2}}{12}

x \to 2 - lim (2 - \frac{1}{x - 2})

\frac{d y}{d x} = \frac{4 x ^{2} + 2 x}{y ^{2}}

f (x) = \frac{1}{x ^{2}}, 1, at x = 1

x \to 7 lim (\frac{x ^{7}}{700})

n = 0 \sum \infty 4 (\frac{3}{5})^{n}

What is the solution for (d^2y)/(dx^2)+2/x (dy)/(dx)=3x+4 ?
The solution for (d^2y)/(dx^2)+2/x (dy)/(dx)=3x+4 is y=c_{1}+(c_{2})/x+(3x^3+8x^2)/(12)